Well first you would need to find a decent router that can transmit the signal with good strength to your basement.
long range wireless router
I have posted about my router and the signal strength i get with it here. It may be the same for you, it may not. It all depends on how the house was built. If there is more or less insulation and things inbetween the floors that can prevent the signal from being transmitted properly. If there is you will need a repeater and signal booster to get it over such a long range.
With that you should know that WiFi is not going to be as fast as wired. Ever. The fastest it is rated at now is 100-200+ mb/s. So that is going to be a lot slower than your FiOS is capable of. That is with N band as well.
Along with that you will have to buy the
XBOX WiFi adapter. That itself is $100. Add that to the router and possible repeater and booster and you are talking a few hundred $ to get this working properly.